### A11. Period with changing depth

In this test we consider an infInite domain with a uniform wave field. An Initial spectrum is given (narrow both in frequency and in direction). In test A11 the current velocity is 0, and the depth varies as function of time (physically impossible since it violates mass conservation). It is seen from theory that wave number and direction of the wave field have to remain constant. A table is written giving depth, wavelength, direction and period (both relative and absolute) as function of time.

The analytical solution for this case is: $T = 2 \pi \left[g k tanh\left(k d\right)\right]-1/2$ (T is absolute period). We use: k0 = 0.1 m-1, d0 = 5 m and θ0 = 120°. It follows that T0 = 20 s.

Since Swan uses a spectrum formulated in terms of relative frequency $\sigma$; there is transport of energy in $\sigma$-direction. Thus there may be a change in the shape of the spectrum due to numerical inaccuracies. Plot file A11.plt shows period, wavelength and direction as function of depth.

The variable depth is obtained by the combination of a constant bottom level, and a time-varying water level which read from file. The uniform field over space is obtained by a combination of a 1-d computation in x-direction, using only a few grid points, and the use of the repeating option.

1 cases is considered:

A11a
time-varying water depth